Crouch has scored seven goals in 29 Premier League appearances for Mark Hughes' men this term, a contribution that has helped Stoke to 10th in the table.
The 33-year-old has an impressive record of 22 goals in 42 appearances for England, but his last cap came in a friendly encounter against France in November 2010.
With Wayne Rooney and Daniel Sturridge almost certain to be in Roy Hodgson's 23-man squad for Brazil 2014, and the likes of Danny Welbeck, Jermain Defoe, Andy Carroll and Rickie Lambert also vying for a spot, Crouch is seemingly well down the pecking order.
However, Begovic, who is set to be Bosnia-Herzegovina's first-choice keeper in the tournament, believes the former Liverpool man - who played at the 2006 and 2010 World Cups - is worthy of representing his country on the biggest stage once again.
Speaking to talkSPORT, he said: "I can't recommend Peter Crouch highly enough.
"I've played with him for a few years at Stoke, and before that at Portsmouth. He offers you something different.
"There are not many strikers like him around the world, it will be very difficult for defences to handle him.
"His goal record speaks for itself, especially at international level. He can make a big difference."
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